scholarly journals Geometry controlled anomalous diffusion in random fractal geometries: looking beyond the infinite cluster

2015 ◽  
Vol 17 (44) ◽  
pp. 30134-30147 ◽  
Author(s):  
Yousof Mardoukhi ◽  
Jae-Hyung Jeon ◽  
Ralf Metzler
Keyword(s):  
Random Walk ◽  
Percolation Threshold ◽  
Anomalous Diffusion ◽  
Infinite Cluster ◽  
Random Fractal

We study the strongly non-ergodic effects of a random walk on a percolation geometry below, at, and above the percolation threshold.

scholarly journals Chover-Type Laws of the Iterated Logarithm for Continuous Time Random Walks

2012 ◽  
Vol 2012 ◽  
pp. 1-13
Author(s):  
Kyo-Shin Hwang ◽  
Wensheng Wang
Keyword(s):  
Random Walk ◽  
Random Walks ◽  
Anomalous Diffusion ◽  
Renewal Process ◽  
Continuous Time ◽  
Waiting Times ◽  
Continuous Time Random Walk ◽  
Domains Of Attraction ◽  
Iterated Logarithm ◽  
Continuous Time Random Walks

A continuous time random walk is a random walk subordinated to a renewal process used in physics to model anomalous diffusion. In this paper, we establish Chover-type laws of the iterated logarithm for continuous time random walks with jumps and waiting times in the domains of attraction of stable laws.

scholarly journals Fractional compound Poisson processes with multiple internal states

2018 ◽  
Vol 13 (1) ◽  
pp. 10 ◽  
Author(s):  
Pengbo Xu ◽  
Weihua Deng
Keyword(s):  
Stochastic Process ◽  
Random Walk ◽  
Waiting Time ◽  
Anomalous Diffusion ◽  
First Passage Time ◽  
Passage Time ◽  
Poisson Processes ◽  
First Passage ◽  
Internal States ◽  
Functional Distribution

For the particles undergoing the anomalous diffusion with different waiting time distributions for different internal states, we derive the Fokker-Planck and Feymann-Kac equations, respectively, describing positions of the particles and functional distributions of the trajectories of particles; in particular, the equations governing the functional distribution of internal states are also obtained. The dynamics of the stochastic processes are analyzed and the applications, calculating the distribution of the first passage time and the distribution of the fraction of the occupation time, of the equations are given. For the further application of the newly built models, we make very detailed discussions on the none-immediately-repeated stochastic process, e.g., the random walk of smart animals.

scholarly journals Random Walk on the Incipient Infinite Cluster for Oriented Percolation in High Dimensions

2008 ◽  
Vol 278 (2) ◽  
pp. 385-431 ◽  
Author(s):  
Martin T. Barlow ◽  
Antal A. Járai ◽  
Takashi Kumagai ◽  
Gordon Slade
Keyword(s):  
Random Walk ◽  
Oriented Percolation ◽  
High Dimensions ◽  
Infinite Cluster ◽  
Incipient Infinite Cluster

A two-dimensional non-Markovian random walk leading to anomalous diffusion

2015 ◽  
Vol 421 ◽  
pp. 522-532 ◽  
Author(s):  
M.A.A. da Silva ◽  
G.M. Viswanathan ◽  
J.C. Cressoni
Keyword(s):  
Random Walk ◽  
Anomalous Diffusion ◽  
Two Dimensional

scholarly journals Probing the type of anomalous diffusion with single-particle tracking

2014 ◽  
Vol 16 (17) ◽  
pp. 7686-7691 ◽  
Author(s):  
Dominique Ernst ◽  
Jürgen Köhler ◽  
Matthias Weiss
Keyword(s):  
Random Walk ◽  
Particle Tracking ◽  
Anomalous Diffusion ◽  
Single Particle ◽  
Single Particle Tracking ◽  
Tracking Data

We introduce a versatile method to extract the type of (transient) anomalous random walk from experimental single-particle tracking data.

scholarly journals Random walk on the incipient infinite cluster on trees

2006 ◽  
Vol 50 (1-4) ◽  
pp. 33-65 ◽  
Author(s):  
Martin T. Barlow ◽  
Takashi Kumagai
Keyword(s):  
Random Walk ◽  
Infinite Cluster ◽  
Incipient Infinite Cluster
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